Question

Marie can afford a $250 per month car payment. She's found a 5 year loan with an annual rate of 7% compounded monthly. How expensive of a car can she afford? How much total money will she pay the loan company? How much of that money is interest?

Answer 1

Marie can afford a 250$ monthly car payment;

The loan is of 5 years (= 60 months) with an annual rate of 7% compounded monthly;
Monthly rate = 7%/12 = 0.5833% = 0.00583

Thus, we know that for monthly payment (EMI)

EMI = P * r * (1+r)ⁿ / (1+r)ⁿ-1 where n = number of months; r = monthly interesr rate and P = principal amount;

so P = EMI* [(1+r)ⁿ-1] / r(1+r)ⁿ = 250 [( 1+0.00583)⁶⁰-1] / (0.00583)(1.00583)⁶⁰
P = 104.335 / 0.008263 = 12626.873;
So, Marie can afford a car of 12,627$


Total money that she will pay to the company = EMI* number of months = 250*60 = 15,000$

Interest paid = 15,000 - 12,627 = 2373$

(we have rounded off the monthly payment to the nearest dollar)